The First Minister and SNP leader hailed the "immense contribution" made by unpaid carers, particularly over the last year during the coronavirus pandemic.
The party is now proposing to make a double payment of the Carers Allowance Supplement this year - worth £460 - in recognition of the additional burden that has been placed on those who look after a loved one.
Ms Sturgeon also said if re-elected to government, the SNP would then seek to introduce a new Carers Assistance payment, to replace the current Carers Allowance.
This would pay out a further £10 a week to those who are caring for more than one disabled person, and would also extend the amount of time that this can be claimed for after the death of someone, from eight weeks to 12 weeks.
In addition to this, the SNP plans to replace the current UK winter fuel payment with a new winter heating payment for older Scots - which would be paid at the same rate and not means tested - helping about one million households a year.
The existing Cold Weather Payment, which is only paid out when the temperature reaches a certain level, would also be replaced with a new annual £50 Winter Heating Payment to those low income households eligible for the current scheme, helping some 400,000 families and individuals.
Speaking about the planned changes to benefits, Ms Sturgeon said: "Unpaid carers make an immense contribution to the health and wellbeing of loved ones, probably never more so than during the last 12 months.
"So, we will make another double payment this year of Carers Allowance Supplement, before replacing the Carers Allowance with an improved Carers Assistance Payment.
"We'll also replace the UK Government's unreliable £25 Cold Weather Payment which only pays out if in certain weather conditions, with a £50 annual payment."
The SNP will reveal more details of its plans for a "fairer Scotland" ahead of the May 6 election, Ms Sturgeon pledged, with these including a minimum income guarantee for all.
She told voters her party was "absolutely committed to leading Scotland through the pandemic, building a fairer Scotland, and supporting all of our citizens through the recovery".
The SNP has already announced plans to double the Scottish Child Payment from £10 a week to £20 a week, if it is re-elected to government.
And Ms Sturgeon sought to contrast the approach of her party with that of the Conservatives at Westminster.
The SNP leader said: "Since the Social Security Act was passed in 2018, the SNP Government has built a brand new social security system from scratch - one that has the principles of dignity, fairness and respect at its heart.
"We're using these new powers to make a real difference to families across Scotland.
"This is an investment in our people, and in Scotland's future - and stands in stark contrast to the Tories' record in government, which has presided over a decade of cuts in support of the very people who need it most, and the frankly disgusting treatment of people with disabilities - as well as policies like the Bedroom Tax and the abhorrent Rape Clause."